基于自适应LQR控制的质子交换膜燃料电池热管理系统温度控制

doi:10.13229/j.cnki.jdxbgxb20220259

Abstract

Abstract:

In order to improve the operation efficiency of fuel cell， its working temperature must be effectively controlled. In this paper， the thermal management system model is built on the Matlab/Simulink platform. The model can be used to analyze the flow distribution， pressure loss and heat exchange between various parts. Based on this model， an adaptive linear quadratic regulator （LQR） controller is proposed and compared with LTI-LQR and LQI controllers under different working conditions. The simulation results show that under the step response test， the adaptive LQR controller has no steady-state error， no overshoot and the rising time is 15 s； under the dynamic performance test， the stack outlet temperature can quickly track the reference value in the global range， which fully reflects the advantages of the controller.

Key words: vehicle engineering, proton exchange membrane fuel cell（PEMFC）, thermal management system, dynamic feedback gain, linear quadratic regulator（LQR）

CLC Number:

U469.72

Yao-wang PEI,Feng-xiang CHEN,Zhe HU,Shuang ZHAI,Feng-lai PEI,Wei-dong ZHANG,Jie-ran JIAO. Temperature control of proton exchange membrane fuel cell thermal management system based on adaptive LQR control[J].Journal of Jilin University(Engineering and Technology Edition), 2022, 52(9): 2014-2024.

Figures/Tables 16

Fig.1

Fig.2

Fig.3

Table 1

Rated working condition parametersof 110 kW stack"

参数	数值	参数	数值
?	0.85	I_st/A	477
A_st/m²	1.5	n_cell	370
T_st/K	356	λ	2
T_amb/K	298	φ	0.21
$Δ T a i r$ /K	10

Table 1

Fig.4

Fig.5

Fig.6

Fig.7

Table 2

Parameters of equilibrium operating point"

参数	序号
参数	1	2	3	4	5
$I s t / A$	100	200	300	400	500
$U / V$	0.79	0.75	0.71	0.68	0.63
$m ˙ c o l$ /（kg·s^-1）	2.47	2.88	3.21	3.53	3.95
$T s t / K$	343.76	351.74	358.91	360.02	361.25
$T s t_e / K$	342.93	350.00	356.15	356.15	356.15
$T r a d_e / K$	310.41	324.22	333.97	339.49	344.38
$T i l o o p_e / K$	342.93	350.00	356.15	356.15	356.15
α	0.085	0.20	0.32	0.55	0.91

Table 2

Table 3

LTI model of each equilibrium operating point"

序号	$I s t / A$	A	$B u$	$B w$	C
1	100	$- 0.4762 0.4762 0 ??????????? 0 ??????????? 2.6582 - 3.4461 0.7209 0.0670 0 ??????????? 4.3254 - 4.3254 0 ??????????? 0 ??????????? 0.1005 0 ??????????? - 0.3663$	$0 ??????????? - 25.6258 0 ??????????? 38.4386$	$3.9384 × 10 - 3 0 ??????????? 0 0 ??????????? 0 0 ??????????? 0 0.2658$	$[0100]$
2	200	$- 0.4762 0.4762 0 ??????????? 0 ??????????? 2.6582 - 3.5769 0.7383 0.1803 0 ??????????? 4.4300 - 4.4300 0 ??????????? 0 ??????????? 0.2705 0 ??????????? - 0.5363$	$0 ??????????? - 23.6780 0 ??????????? 35.5163$	$2.8860 × 10 - 3 0 ??????????? 0 0 ??????????? 0 0 ??????????? 0 0.2658$	$[0100]$
3	300	$- 0.4762 0.4762 0 ??????????? 0 ??????????? 2.6582 - 3.6820 0.6933 0.3306 0 ??????????? 4.1598 - 4.1598 0 ??????????? 0 ??????????? 0.4959 0 ??????????? - 0.8016$	$0 ??????????? - 22.7106 0 ??????????? 34.0659$	$2.8857 × 10 - 3 0 ??????????? 0 0 ??????????? 0 0 ??????????? 0 0.2415$	$[0100]$
4	400	$- 0.4762 0.4762 0 ??????????? 0 ??????????? 2.6582 - 3.7829 0.4731 0.6517 0 ??????????? 3.0408 - 3.0408 0 ??????????? 0 ??????????? 0.9269 0 ??????????? - 1.2990$	$0 ??????????? - 18.7379 0 ??????????? 28.1068$	$4.6103 × 10 - 3 0 ??????????? 0 0 ??????????? 0 0 ??????????? 0 0.3721$	$[0100]$
5	500	$- 0.4762 0.4762 0 ??????????? 0 ??????????? 2.6582 - 3.9182 0.1086 1.1514 0 ??????????? 0.6517 - 0.6517 0 ??????????? 0 ??????????? 1.7270 0 ??????????? - 2.1656$	$0 ??????????? - 13.5515 0 ??????????? 22.2447$	$4.8587 × 10 - 3 0 ??????????? 0 0 ??????????? 0 0 ??????????? 0 0.4386$	$[0100]$

Table 3

Fig.8

Table 4

K value of each equilibrium operating point"

序号	$I s t$ /A	$K$
1	100	$- 1.0664 ??? - 9.6349 ?? - 0.0675 ??? 0.2338 ? - 1$
2	200	$- 1.0745 ??? - 9.6196 ?? - 0.0700 ??? 0.2288 ? - 1$
3	300	$- 0.9893 ?? - 9.6083 ?? - 0.0694 ??? 0.2223 ?? - 1$
4	400	$- 0.9566 ?? - 9.5642 ?? - 0.0665 ??? 0.2068 ?? - 1$
5	500	$- 1.1747 ?? - 9.4207 ?? - 0.0708 ??? 0.1896 ??? - 1$

Table 4

Fig.9

Fig.10

Fig.11

Fig.12

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Temperature control of proton exchange membrane fuel cell thermal management system based on adaptive LQR control

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